A cost variance is the difference between a pre-established measure of a cost and the actual measure of it, and the formula that computes one depends on which of two systems is asking. Standard costing splits the difference into a price component and a quantity component, and computes each separately. Earned value management computes one figure: the budgeted cost of the work performed, minus what that work actually cost.
Both families are in current use and both are called cost variance, which is why the same search returns a manufacturing formula and a project management formula side by side. What a variance is, the sign convention that makes one favorable or unfavorable, and where variance review lands in a firm’s close are set out in variance accounting. This entry is the formulas themselves.
The Two-Part Split Behind Every Standard Cost Formula
Every standard cost formula in this family comes out of one structural fact: a standard cost is built by multiplying a price measure by a quantity measure, so a difference from it can always be attributed to the price leg, the quantity leg, or both.
The federal Cost Accounting Standards define both legs for both inputs. Material cost at standard is a pre-established measure of the material element of cost, computed by multiplying material-price standard by material-quantity standard, and labor cost at standard is the same construction, computed by multiplying labor-rate standard by labor-time standard (48 CFR 9904.407-30). The four component standards behind them, and the meaning of a variance struck against one, are set out in variance accounting.
The rules also allow a hybrid. Where only one of material price or material quantity is set at standard and the other is stated at actual, the result of the multiplication is still treated as material cost at standard, and the same holds where only the labor rate or the labor time is set at standard (48 CFR 9904.407-50(a)(2)). A system that standardizes only rates is still a standard cost system.
The Material Formulas
Total cost variance = actual cost - standard cost for output achieved
Material price variance = (actual price - standard price) x actual quantity
Material quantity variance = (actual quantity - standard quantity) x standard price
Material cost variance = material price variance + material quantity variance
(once both are struck on the same quantity)The standards name all three, and condition the combination on the price variance first being allocated to a production unit (48 CFR 9904.407-50(b)(5)).
The price leg carries the price gap on actual quantity; the quantity leg carries the quantity gap at standard price. That is not a convention picked for tidiness, it is what stops the same dollar being counted in both. Which quantity sits in the price leg depends on when the variance is struck, quantity purchased if it is recognized at purchase and quantity used if it is recognized at issue, and the consequences of that choice are in purchase price variance.
The Labor Formulas
Labor rate variance = (actual rate - standard rate) x actual hours
Labor time variance = (actual hours - standard hours allowed) x standard rate
also called the labor efficiency variance
Labor cost variance = labor rate variance + labor time varianceThe structure is identical to materials, with rate standing in for price and time for quantity. The regulation permits the same combination: labor-rate variances and labor-time variances may be combined into one labor-cost variance account, and a separate labor-cost variance is accumulated for each production unit (48 CFR 9904.407-50(c)).
Standard hours allowed is the phrase that gets misread. It is not the hours budgeted at the start of the period. It is the standard time for the output actually produced, so the flexible measure moves with volume and the variance isolates efficiency rather than activity level. Where a firm needs the overhead equivalent of this split, it is in 2-way variance analysis.
Timing Decides What the Formula Is Measuring
The same arithmetic answers a different question depending on when it runs, and the standards make the timing an explicit choice for materials and a fixed rule for labor.
Materials give a timing choice, at purchase or at issue, and that choice is worked through in purchase price variance. Recognizing at purchase isolates a purchasing decision at the moment it is made; recognizing at issue ties the variance to the job that consumed the material.
Labor is not optional. Labor-cost variances are recognized at the time labor cost is introduced into production units (48 CFR 9904.407-50(c)). Labor cannot be stockpiled, so there is no earlier moment to catch it in.
The Earned Value Cost Variance
The project management formula is a single subtraction, and it compares work done against money spent rather than price against quantity.
Cost variance is the difference between completed work, the budgeted cost of work performed, and its cost, the actual cost of work performed, while schedule variance is the difference between completed work and planned work. Positive variances indicate the program is either underrunning cost or performing more work than planned, and negative variances the reverse (GAO, Cost Estimating and Assessment Guide, GAO-20-195G, Chapter 19).
Cost variance = BCWP - ACWP (earned value - actual cost)
Schedule variance = BCWP - BCWS (earned value - planned value)Two things separate this from the standard cost family. The comparison is against the budget for work genuinely finished rather than against a per-unit standard, which is what keeps a project that has spent half its money on a tenth of its scope from looking on budget. And the direction is fixed by the definition, so a negative number is the bad one, where standard costing has no such fixed convention and a variance report has to state which direction it is calling favorable (variance accounting).
This is the version US federal contractors meet. An earned value management system is required for major acquisitions for development, and an offeror whose system has not been determined compliant with Electronic Industries Alliance Standard 748 must submit a comprehensive plan for compliance, though offerors are not eliminated from consideration for award for lacking a compliant system (48 CFR 34.201).
Common Questions
Ask which system first, because the two answers are different. In standard costing the total cost variance for an input is the actual cost of that input minus its standard cost for the output achieved, and it decomposes into a price or rate variance plus a quantity or time variance. In earned value management the cost variance is the budgeted cost of work performed minus the actual cost of work performed, with no decomposition. A formula quoted without naming its system is the most common way this goes wrong on a client engagement.
A rate variance is one component of a cost variance, not an alternative to it. The cost variance for direct labor is the whole difference between what the labor cost and what it should have cost; the rate variance is the part of that difference caused by paying a different hourly rate than standard, and the time variance is the part caused by using a different number of hours. The two components sum back to the total, which is the arithmetic check on the split.
Accountably places trained offshore accountants and tax preparers inside US CPA and EA firms, and a firm can put a real block of its own close and variance reporting through a trial task before a client engagement depends on it.
